SUBJECT
Advanced cryptography
lecture + practical
master
6
Semester 1/3
Autumn semester
The course have two main goals: discovering the mathematical background beyond several cryptographic constructions and introducing novel cryptographic primitives using interesting results from various topics of mathematics or computer science. For the first part, we present the necessary exact definitions, precise assumptions and rigorous proofs of security. For the second part, we present recent results, methods and its connections to cryptographic problems from finite fields to linear algebra.
Perfect and computational security, proofs by reduction, security definitions, pseudorandomness, message authentication codes, collision-resistant hash functions, one-way functions, cryptographic hardness assumptions, primality testing, factoring and computing discrete logarithms, arithmetics in finite fields and its applications, elliptic curve based cryptography, lattice based constructions, secure multiparty computation, secret sharing problems, applications for e-commerce.
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Berlekamp, E.R.: Algebraic Coding Theory. McGraw Hill, 1968
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Huffman, W.C. –Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, 2003
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van Lint, J.H.: Introduction to coding theory. Springer Verlag, 1982
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McWilliams, F.J. –Sloane, M.J.A.: The theory of error-correcting codes. North-Holland, 1977
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Roman, S.: Coding and information theory. Springer Verlag, 1992
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Beutelspacher, A.: Cryptology. The Mathematical Association of America, 1994
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Brassard, G.: Modern cryptology. Springer Verlag, 1988
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van Tilborg: An introduction to cryptology. Kluiver Academic Publisher, 1988